# Remainder Calculator

URL: https://speedycalculator.com/calculators/math/remainder/
Last updated: 2026-10-30

> The remainder calculator divides one integer by another and gives the quotient and the remainder, with a check that dividend = divisor × quotient + remainder.

## Inputs

- Dividend
- Divisor

## Results

- Remainder
- Quotient
- Check: divisor × quotient + remainder

## Formula

```
Remainder = dividend − divisor × ⌊dividend ÷ divisor⌋
```

## Explanation

Remainders answer "how many are left over?" – 17 eggs in boxes of 6 leave 5. They also decide odd and even, days of the week and clock times.

### How to use the Remainder Calculator

- **Dividend**
- **Divisor**

Results update as you type, and everything is calculated in your browser.

### How it works

The quotient is the whole number of times the divisor fits; the remainder is what is left and is always smaller than the divisor.

### Inputs explained

FieldWhat to enterDividendA numberDivisorA number

### What each result means

- **Remainder** = [Dividend] - [Divisor]×floor([Dividend]÷[Divisor])
- **Quotient** = floor([Dividend]÷[Divisor])
- **Check: divisor × quotient + remainder** = [Divisor]×floor([Dividend]÷[Divisor]) + ([Dividend] - [Divisor]×floor([Dividend]÷[Divisor]))

### Example values

How the main result changes when **Dividend** changes and everything else stays at the example values above:

DividendRemainder8.52.512.750.7517521.253.2525.51.5344

## Worked example

Inputs — Dividend: 17; Divisor: 6.

Results — **Remainder = 5**; Quotient = 2; Check: divisor × quotient + remainder = 17.

## Key terms

- **Remainder**: The amount left after whole-number division.

## FAQ

**What is the remainder of 17 ÷ 6?**
5.

**Can the remainder be larger than the divisor?**
No – if it were, the divisor would fit once more.

**What does a remainder of 0 mean?**
The divisor divides the dividend exactly.

**How is the remainder written?**
17 ÷ 6 = 2 R 5.


## Sources

- [OpenStax – Prealgebra 2e](https://openstax.org/details/books/prealgebra-2e)
- [OpenStax – Contemporary Mathematics](https://openstax.org/details/books/contemporary-mathematics)